Multiple resonant manipulation of qubits by train of pulses

TL;DR

This paper develops a systematic approach using Bloch vector and Magnus formalism to analyze qubit manipulation by pulse trains, revealing dynamics like quasienergy formation and oscillation patterns in various excitation regimes.

Contribution

It introduces a comprehensive method for studying qubit control with pulse trains, including the formation of quasienergetic states, which advances understanding of quantum manipulation techniques.

Findings

Quasienergetic states form under train pulse excitation.

Qubit transition probabilities show aperiodic and periodic oscillations.

Population dynamics depend on pulse sequence and phase shifts.

Abstract

We present a systematic approach based on Bloch vector's treatment and the Magnus quantum electrodynamical formalism to study qubit manipulation by a train of pulses. These investigations include one of the basic processes involved in quantum computation. The concrete calculations are performed for tunneling quantum dynamics, multiple resonance and off-resonance excitations of qubit driven by Gaussian pulses. In this way, the populations of qubit states due to multiple resonant interactions are investigated for various operational regimes including: single-pulse excitation, two-pulse excitation with phase shift between pulse envelopes being controlling parameter and for excitation with sequential pulses. In the last case, we demonstrate the formation of quasienergetic states and quasienergies of qubit driven by train of identical pulses. In this case the transition probability of qubit exhibits aperiodic oscillations, but also becomes periodically regular for definite values of the quasienergy.